I also tried to change the settings via scenario editor, but that's not working. I can change the settings from 'island' to 'normal', but the generation won't change. What do I need to do to change the map generator?

Note that that sets it to the 0.16 generator, which is not available in the vanilla map generator screen. Furthermore, note that already generated chunks are not affected by changing the map generation settings. You will have to delete the chunks. There are mods available on the mod portal that allow you to delete empty chunks, or you can use another console command: https://wiki.factorio.com/Console#Delete_chunks

That save doesn't have the generator changed to non-island. Furthermore, it looks like something generated the chunks around your island in a huge radius, so you will only get water until you go very far out:

You can solve all of this with the console command to delete chunks (or by using a mod). This is the result of running the console command, if you run it after changing the generator, the black area will generate with the new elevation setting:

/c local surface = game.player.surface;
game.player.force.cancel_charting(surface);
local chunk_radius = 40;
for chunk in surface.get_chunks() do
if (chunk.x < -chunk_radius or chunk.x > chunk_radius or chunk.y < -chunk_radius or chunk.y > chunk_radius) then
surface.delete_chunk(chunk)
end
end